Last week, a pair of polls marked a depressing new low in what feels like the never-ending descent of American politics — and some news from Congress reveals why it will continue. Together, they succinctly explain Washington’s epic dysfunction.

A Quinnipiac University poll found that President Obama’s approval rating has hit an all-time low of 39 percent, while Gallup found that Congress’ approval rating has fallen to 9 percent, the lowest since the Nixon administration. These miserable numbers are driven by two distinct trends: The gradual implosion of the Republican Party over the last year and the sudden collapse of President Obama’s health care law over the last month.

The first trend has been the reigning Washington storyline practically since the defeat of Republican presidential nominee Mitt Romney.

Republicans responded to the loss with a brief, hopeful bout of introspection that culminated with the Republican National Committee calling on the party to pass comprehensive immigration reform and broaden its appeal. But this vision of renewal was quickly subsumed by the familiar opposition to Obama, which deepened and intensified, and eventually led to the government shutdown. Last month, Republican popularity hit a new low.

But as the Quinnipiac poll shows, Republicans’ political fortunes haven’t suffered all that much as a result. Remarkably, less than a month after the end of the shutdown that they brought about, congressional Republicans are more trusted than Obama to handle almost every major policy issue: health care (43 to 42 percent), the economy (45 to 41 percent), immigration (41 to 40 percent) and the federal budget (45 to 40 percent).

How can it be that a party caught in the throes of a civil war and less popular than Nixon during Watergate is still preferred by most Americans?

The answer lies in the other trend.

The debacle of the Obamacare rollout and the president’s less-than-truthful statement — “If you like your health care plan, you can keep it” — have undermined the public’s trust in him. For the first time, a majority of Americans say that Obama is not honest and trustworthy (52 to 44 percent). As Tim Malloy, assistant director of the Quinnipiac University Polling Institute, put it, “Any elected official with an eight-point trust deficit is in serious trouble.”

For Republicans, this is an amazing stroke of good fortune — or at least, it ought to be. Even after Republicans failed to beat Obama at the ballot box or through the shutdown, and sustained enormous damage in the process, the American public is essentially rolling out a red carpet and beckoning them forward anyway.

But a story last week illustrated why Republicans probably won’t be able to take advantage of this opening. Before the shutdown and the Obamacare collapse eclipsed everything else, this fall’s big event was supposed to be the push for corporate tax reform.

House Ways and Means Committee Chairman Dave Camp, of Michigan, has been beavering away on the Republican plan for months and was preparing to unveil it. But as Roxana Tiron and Richard Rubin of Bloomberg News report, “Republican leaders are worried about political damage if the party’s top tax writer releases a plan to revise the U.S. tax code and limit popular breaks.” So they’re trying to stop it.

Let that one sink in for a moment: Republican leaders are trying to block their own tax-reform plan for fear that it will prove too extreme and inflict further damage on the party. And when they do work up the courage to put forward aggressive legislation, they frequently discover that they cannot muster enough Republican support to pass it.

That has often been the case when Republican leaders have attempted to implement their own budget. Over the summer, the House farm bill failed for this reason, and so did a housing and transportation bill a month later. Usually, when Congress is divided, the parties pass their agenda through the chamber they control and the hard part is reconciling the two. What House Republicans have demonstrated is that they can’t enact an agenda even when they’re in charge.

Woven together, these threads tell the story of Washington’s ongoing ineptitude: Americans are fast losing faith in the president, his party and his signature policy achievement. But while they’re open to the idea of handing power to the opposition, Republicans are busy demonstrating that they have no idea how to govern.